Disjoinable Lagrangian tori and semisimple symplectic cohomology

Li, Yin

doi:10.2140/agt.2020.20.2269

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Disjoinable Lagrangian tori and semisimple symplectic cohomology

Yin Li

Algebraic & Geometric Topology 20 (2020) 2269–2335

DOI: 10.2140/agt.2020.20.2269

Abstract

We derive constraints on Lagrangian embeddings in completions of certain stable symplectic fillings whose symplectic cohomologies are semisimple. Manifolds with these properties can be constructed by generalizing the boundary connected sum operation to our setting, and are related to birational surgeries like blow-downs and flips. As a consequence, there are many nontoric (noncompact) monotone symplectic manifolds whose wrapped Fukaya categories are proper.

Keywords

symplectic cohomology, symplectic filling, flip

Mathematical Subject Classification 2010

Primary: 53D05, 53D35, 53D37, 53D40, 53D45

References

Publication

Received: 28 April 2017

Revised: 26 June 2019

Accepted: 7 December 2019

Published: 4 November 2020

Authors

Yin Li
Department of Mathematics King’s College London London United Kingdom

Volume 20, issue 5 (2020)